When I have kept fish in the past, being ambiguous to the gender of my fish bothered me a little. Thankfully, with typical bettas, you can immediately know the gender of your fish!
Like any animal species, male and female bettas differ in general characteristics. Males are much more popular because of their long, especially colorful fins. Females, though, come in a variety of colors as well and can actually live in groups sometimes, while male bettas cannot live together under any circumstance. Here I will describe the basic information of male and female betta characteristics, plus an introduction into betta breeding.
Males
Again, bred male bettas have longer fins and are often considered more beautiful (keep in mind that long tails are a selective breeding trait; wild bettas are more like the plakat tail bettas on this page). They are usually bigger than females, unlike most other fish species. They act more aggresively than females do. Because of their longer fins, males can rip their fins more easily than females. Unless you are especially geared toward owning a female betta, I strongly suggest that your first betta be male. The experience can be more fun with the beautiful fins and such, but males actually do something special that is a sure-fire sign that he is happy. Males create bubble nests (see picture at right) when they are happy in their environment by gulping some air, covering it with saliva, and spitting it out. I remember when I came home one day to find that my male had blown his first nest, and it was such a nice thing to know that he was happy in his new home. It is not necessarily a bad thing if your male does not blow a nest at some point; he may be too young to breed (a male that creates nests is at a good age to breed), or too old to breed, or just won't in general. When stimulated by sight of a female, a male may rapidly create nests. Each bubble is a space that a potential betta egg (from the female) could grow inside. Actually, a female will often not mate with a male unless he already has a nest blown (a good lesson for us women!). And no, these bubbles are not soap. Do not panic and think that there are chemicals on the surface. :)
Most people don't know, though, that male bettas come in a short-tailed variety which is much closer to how males look in the wild. The short finned ones resemble what we usually think of as females and are called plakat (pronounced plah-COT) bettas. Every once in a while a plakat male is mistaken to be a female, and read on in the "female" section to learn the sure-fire way to know...
Females
Female bettas, while still aggressive, can live in schools when there are six or more of them. However, a bowl is not the proper place for an entire school of fish, so people with multiple bettas should have real tanks, minimum 10 gallon. Fewer than six females in a "sorority tank" will result in too much of a pecking order and a "queen bee" fish will make herself known and probably bully the others. The link above is to the BettaBlog, as I'm thinking of starting a sorority tank soon.
Females are smaller than males and do not get injured quite as easily since they don't have to worry about long, elaborate fins. Females may blow bubbles but these are not really bubble nests; only males are capable of blowing full nests. The only sure-fire way to know if your betta is female or a Plakat male (short-finned male) is to see if it has an ovipositor, or the place where eggs come out of females. See a picture of it at left. The ovipositor is a small round dot on the bottom of a betta's belly. When a female is ready to breed, the ovipositor will seem a little more pronounced. She will also display horizontal bars on her body.
Breeding
Betta breeding, unlike general betta keeping, is both time and space consuming and is nearly impossible to make a profit from. Some people breed bettas just for the heck of it just to find that their bettas end up producing 600 babies which will all eventually need separate bowls. Of course, this number of fry (baby bettas) is nearly impossible to accommodate and can become very expensive. Some baby bettas are actually used as food for other kinds of fish. My general disclaimer is this: do not even attempt to breed bettas unless you have the time, money, space, and resources to do so, and do it only after conducting very in-depth research on the matter.
Even if you don't plan on breeding bettas, it's an interesting process which is worth learning about...
When a betta sees another betta, he will flare his gill cover, called the operculum, and make himself look sort of like a lion. This is called flaring or displaying. Bettas do it when they see themselves in a mirror (thinking that it is another fish) or when they see other fish in other bowls. Spending some time each day flaring is actually very good for bettas; they use up some energy daily. When I only had one betta, I let him look at himself in a mirror for about fifteen minutes a day, and I strongly suggest doing this for your betta, male or female, as well. Do make sure not to let this go on too long, though, because they can actually hurt themselves in this aggressive behavior if it goes on for extended periods. Now, I put my female's bowl next to one of my male's bowl and let them flirt for a while. Females will technically flare just like males, but their operculum is smaller.
When two bettas breed, there is a "courtship" period in which the two will bully each other, especially the male to the female. Sometimes the bullying actually leads to death due to the general aggressive behavior of the species. After this courtship, which can last for hours or even days, the two will spawn (see below): they will begin circling
each other under the bubble nest and the female will release eggs. The male will fertilize the 10 to 40 eggs that the female releases during each embrace, and the two will spawn until the female is exhausted of eggs. The eggs will fall to the bottom, and the male will begin to pick them up in his mouth and put each one into an individual bubble in his nest. Sometimes the female will even help out with this job, and it's an amazing sight to see them working together. However, just as often the female will begin to eat the eggs, so many breeders remove the female once she has released eggs. The eggs will stay in the bubbles and grow for a matter of days and then will begin to fall out. Breeders usually take the male out by this time because he many eat the babies as they fall. They will grow quickly and will begin to show characteristics of their sex and become aggressive, so they usually have to be separated soon after they come out of their eggs. They have to be fed on a diet of tiny live food which is difficult to feed and risky for them to eat. They reach maturity at around five or six months, and the average petstore betta is six months old.
Fry grow remarkably quickly and are a delight to watch. Most will gain the majority of their characteristics by the time they are eleven weeks old. I found the diagrams below to be really interesting:
...-..Betta egg: 0.03 inches in diameter
....One day old fry: 0.1 inch long (The tail doesn't show at this scale)
...One week old: 0.2 inches long.
Two weeks old: 0.25 inches long. (Starting to show dorsal fins.)
Three weeks old: 0.34 inches long
Four weeks old: 0.45 inches long on average.
Five weeks old: 0.6 inches long. Size ranges from .5 to .75 inches.
Six weeks old: 0.85 inches long. The largest are over an inch.
Seven weeks old: 1.1 inches long.
Eight weeks old: 1.3 inches long.
Nine weeks old: 1.55 inches long.
Ten weeks old: 1.7 inches long
Eleven weeks old: 1.9 inches long
After this point, the body won't grow too much more but the fins will grow slowly until the fish is about seven months old.
Further Reading:
http://www.aquariumfish.net/catalog_pages/bettas/betta_breeding.htm
http://www.bettatalk.com/how_bettas_spawn.htm
http://www.aquarticles.com/articles/breeding/kick_beta-breeding.html
Pictures: